What are number series questions?

Number series questions give you a sequence of numbers that follow a hidden rule. Your job is to figure out the pattern and predict the next number. They make up roughly one-third of the numerical reasoning section on the PI Cognitive Assessment, which means you’ll see about 5-6 of them on a full 50-question test.

The key to number series is speed. You have roughly 14 seconds per question. If you can recognize the pattern type within the first 5 seconds, you’ll have enough time to calculate the answer.

Here are the most common patterns and how to spot them.

Constant difference (addition or subtraction)

The simplest pattern. Each number increases or decreases by the same amount.

Example: 3, 7, 11, 15, 19, ___

Look at the differences: +4, +4, +4, +4. The answer is 23.

How to spot it: Calculate the difference between the first two numbers. If the same difference holds for the next pair, you’ve found it. Takes about 3 seconds.

Constant multiplier (multiplication or division)

Each number is multiplied (or divided) by the same factor.

Example: 2, 6, 18, 54, ___

The pattern: each number is multiplied by 3. The answer is 162.

How to spot it: If the numbers grow quickly (doubling, tripling), try dividing each number by the previous one. If you get the same result, that’s your multiplier.

Increasing differences

The difference between consecutive numbers grows by a constant amount.

Example: 3, 5, 9, 15, 23, ___

Differences: +2, +4, +6, +8. The differences increase by 2 each time. The next difference is +10, so the answer is 33.

How to spot it: Calculate differences. If they’re not constant, calculate the differences of the differences. If those are constant, you’ve found an increasing-difference pattern.

Alternating patterns

Two separate sequences are interleaved into one.

Example: 2, 10, 4, 20, 6, ___

Split into odd positions (2, 4, 6) and even positions (10, 20). Odd positions increase by 2. Even positions increase by 10. The next number is in an even position: 30.

How to spot it: If the pattern doesn’t make sense as a single sequence, try looking at every other number separately. This is often the trickiest pattern to recognize under time pressure.

Fibonacci-variant patterns

Each number is the sum of the two numbers before it (or a variation of this rule).

Example: 1, 1, 2, 3, 5, 8, ___

Each number = sum of previous two. 5 + 8 = 13. The answer is 13.

How to spot it: If neither differences nor ratios reveal a pattern, try adding consecutive pairs. Fibonacci variants are less common on the PI Cognitive Assessment but they do appear.

Solving strategy for the test

When you see a number series question on the PI Cognitive Assessment, follow this process:

Check differences first. Calculate the gaps between consecutive numbers. If they’re constant, you’re done. If they’re increasing by a constant amount, you’re done. This handles about 60% of number series questions.
Check ratios. If differences don’t work, try dividing each number by the previous one. If you get a constant ratio, multiply to find the answer.
Check alternating. If neither works, look at odd and even positions separately.
If nothing clicks in 10 seconds, guess and move on. Some number series have complex nested rules. Spending 30 seconds on one question costs you two easier questions elsewhere.

Practice examples

Try these. Answers are below.

5, 10, 15, 20, 25, ___
4, 12, 36, 108, ___
1, 4, 9, 16, 25, ___
7, 3, 8, 3, 9, ___
2, 3, 5, 8, 13, ___

Answers:

30 - constant difference of +5
324 - constant multiplier of x3
36 - perfect squares (1, 4, 9, 16, 25, 36). Differences increase: +3, +5, +7, +9, +11
3 - alternating pattern. Odd positions: 7, 8, 9 (+1). Even positions: 3, 3, 3 (constant)
21 - Fibonacci variant. Each number is the sum of the previous two (8 + 13 = 21)

Number Series: Patterns and Practice